Systems can be defined generally as an object in which signals interact to produce an observable output signal. The system can be a physical entity, such as a chemical process, an electrical circuit, or an engine. The system can also be an abstract entity, such as the stock market or a financial system. One important type of system is the multiple input, multiple output (MIMO) system. As the name suggests, a MIMO system has multiple inputs and multiple outputs, in contrast to single input, single output (SISO) systems. MIMO systems are commonly controlled using model-based control methods, such as linear quadratic (LQ) control or model predictive control (MPC).
Model predictive control is the dominant advanced control method in process industries for control of large-scale MIMO processes. MPC systems use a model of the MIMO system and make control decisions based on the model. MPC systems are popular for complex systems because they can explicitly optimize the process, handle complex multivariate processes, and account for system constraints, such as valve motion limits. In spite of these benefits, existing MPC systems present problems that prevent widespread use. MPC systems run too slowly for large-scale processes, processes with long time delays, and processes with fast sampling times. MPC systems also run too slowly when the problem being solved has long control horizons. Specific problems that cause the MPC systems to run slowly include solution tables becoming so large as to prevent searching in a reasonable time and solution tables lacking the optimal solution. Performance of the MPC system often suffers when a suboptimal solution is used.
Previous attempts to use MPC systems for complex MIMO processes have used complete enumeration strategies, i.e., strategies which solve the MIMO system over the whole parameter region for all possible solutions. One example of a complete enumeration strategy for solving the MPC systems formulated as quadratic programs is a multi-parametric quadratic programming solver technique, which can use active set techniques or interior point quadratic programming solver techniques to compute the optimal solution for each current parameter. The number of computations involved in these complete enumeration strategies grows rapidly with the number of dimensions and length of the horizon, making the strategies slow to run and unsuitable for real time control of complex MIMO processes.
It would be desirable to have a partial enumeration model predictive controller that would overcome the above disadvantages.